http://sports.ha.com/c/item.zx?saleN...46#88198819224
Take a look at this lot of 1912 stubs offered through Heritage a while back, one of which has the full paragraph of "fine print" at the bottom that is mostly torn off of yours. It reads:
"If legal game is not played, this check may be changed at Box Office for admission to any American League game on these grounds during 1912."
Based on my reading of that, while it is clear that your ticket was used for admission to a game, there is no way to determine exactly what game it was used for, as it could have been used for any game during the remainder of the 1912 season. Unless they had a particular way of marking the stub to indicate the date it was used (which doesn't appear to be the case), it looks to me like the write-up that PSA gave it is as specific as they can get.